TrainSum

class trainsum.trainsum.TrainSum(namespace: Any)

Parameters:

namespace (ArrayNamespace)

namespace: ArrayNamespace

Array namespace for the underlying array library.

index_type: Any

Internally used index type.

Basics

TrainSum.dimension	Quantized dimension, defined by a sequence of digits.
TrainSum.domain	Domain, defining a one dimensional interval.
TrainSum.uniform_grid	Uniformly N-dimensional spaced grid.
TrainSum.trainshape	Base class describing the shape of a quantics tensor train.
TrainSum.svdecomposition	Singular value decomposition for matrices.
TrainSum.rand_svdecomposition	Randomized singular value decomposition for matrices.
TrainSum.qrdecomposition	QR decomposition for matrices.
TrainSum.sweeping_strategy	Strategy for sweeping through a tensor train.

Construction

TrainSum.full	\(f(x)=v\).
TrainSum.exp	\(f(x)=e^{a(x-x_0)}\).
TrainSum.sin	\(f(x)=\sin{\left(a(x-x_0)\right)}\).
TrainSum.cos	\(f(x)=\cos{\left(a(x-x_0)\right)}\).
TrainSum.polyval	\(f(x)=\sum_i{v_i(x-x_0)^i}\).
TrainSum.shift	Generic shift matrix.
TrainSum.slice_vector	Binary vector defined by a slice.
TrainSum.slice_operator	Binary operator defined by a slice.
TrainSum.toeplitz	Three dimensional Toeplitz tensor.
TrainSum.tensortrain	Construct generic quantics tensor trains from some provided data.

Binary Tensor Trains

TrainSum.linear_integer_equation	Linear integer equation: \(\sum^N_i c_i x_i = \Delta\).
TrainSum.modulo_integer_equation	Modulo integer equation: \(\sum^N_i c_i x_i \mod m = \Delta\).
TrainSum.range_integer_equation	Range integer equation: \(l_i \leq x_i \leq u_i\).
TrainSum.binary_train	Construct a tensor train from a sequence of integer equations.

Discrete Wavelet Transform

TrainSum.dwt	Wavelet transformation matrix as a quantics tensor train.
TrainSum.idwt	Inverse wavelet transformation matrix as a quantics tensor train.

Fourier Transform

TrainSum.qft	Quantum fourier transformation matrix as a quantics tensor train.
TrainSum.iqft	Inverse quantum fourier transformation matrix as a quantics tensor train.
TrainSum.qftshift	Shift the zero frequencies to the middle of the spectrum.
TrainSum.iqftshift	Inverse of the qftshift.
TrainSum.qftfreq	Sample frequencies for the quantum fourier transform.

Input/Output

TrainSum.write	Write a quantics tensor train or a uniform grid to a hdf5 group.
TrainSum.read	Read a quantics tensor train or a uniform grid to a hdf5 group.

Solver

TrainSum.gmres	GMRES iterative linear solver.
TrainSum.lanczos	Lanczos iterative eigenvalue solver.
TrainSum.eigsolver	Variational eigenvalue solver for quantics tensor trains.
TrainSum.linsolver	Variational linear solver for quantics tensor trains.

Operations

TrainSum.outer	Form the outer product of multiple tensor trains by fusing them.
TrainSum.min_max	Calculate the minimum and maximum values and indices.
TrainSum.add	Add multiple tensor trains.
TrainSum.einsum	Perform an einsum operation.
TrainSum.einsum_expression	Create an einsum expression to be used with tensor trains.
TrainSum.evaluate	Perform an evaluation at idxs of an einsum expression.
TrainSum.evaluate_expression	Create an evaluation expression to be used with tensor trains.

Context Manager

TrainSum.exact	Exact einsum operations.
TrainSum.decomposition	Einsum operations based on matrix decompositions.
TrainSum.variational	Variational einsum operations.
TrainSum.cross	Manager for cross interpolation based operations.
TrainSum.evaluation	Manager for evaluate operations.
TrainSum.set_options	Set options globally.
TrainSum.get_options	Get the current options.